When I was in UCLA's Statistics program, I did an independent study class with him, where we met in his sunny office once a week. At the time, I had only a vague idea of his reputation -- he was just "that guy who had his own theorem," who was excited to answer my questions about game theory.
I asked him to give me an intuitive explanation of Nash's theorem, and, while the details are lost to memory, I remember having one of those thrilling epiphanies as he explained how it followed from Brouwer's fixed point theorem.
There was supposed to be required coursework, but every week I'd come into his office and ask questions like that, and we'd end up talking the whole time, often long after the hour was over. Grades and homework didn't seem to matter much to him. It's incredible to think now how much excitement and passion he mustered for the curiosity of a novice.
RIP, Prof Shapely.